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arXiv · 1801.01699

Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance

Jun Yoshizawa·Shota Saito·Toshiyasu Matsushima
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Abstract

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $\epsilon$-variable-length resolvability. We derive the general formula of the $\epsilon$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant $\epsilon$. Our result clarifies a dual relationship between the general formula of $\epsilon$-variable-length resolvability and that of $\epsilon$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

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Jun Yoshizawa, Shota Saito, Toshiyasu Matsushima. 2018-01-05. Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance. https://arxiv.org/abs/1801.01699

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